While scheduling the month of June for the site, and considering the potential for some likely downtime or errors while changing web hosts, I budgeted two weeks for recent US championship puzzle discussion. For this week, I’ve planned to cover the US Sudoku Qualifying Test (also the sixth leg of the Sudoku Grand Prix). If you are desperate for new puzzles, those will arrive next Monday at their usual time. But there may be some new challenges revealed throughout this week during the discussion of these creative sudoku.

I figured I’d give a general overview of our design process at the start. As with past years, we (Nick Baxter, Wei-Hwa Huang, and myself) had planned a two-part championship with Classics and near classic variations for the first part, and mostly new or less common styles for the second part. Some of this has been to gauge relative solving capabilities on the challenges that might appear at a WSC, and some of this has been for our own sanity checking of potential competitors. There are more web-accessible sudoku solving tools that can handle “part 1” puzzles and some unbelievable times have been posted there in the past. But less familiar or original styles in “part 2” will challenge anyone solving with certain types of assistance. After the 2009 experiences in Philadelphia at our last live national championship, we know to be extra cautious.

While having two parts was the original plan, the requirements of the Grand Prix changed our design mid-stream and a single big round was used instead. So solvers got 2.5 straight hours of solving to test their mettle. But you can see that the ordering of the puzzles still naturally splits the first ten from the last ten and perhaps many solvers found themselves focusing on just the first part instead of the other.

We like having a mix of puzzles but also a fair number of classic sudoku since a sudoku championship should certainly test the fundamentals. I wrote all 4 of our classic puzzles, each somewhat noteworthy in its own way. Their numbering was maintained in my “construction order”, as testing revealed their mean solve times were within a minute of each other and they would all receive the same point values on the test. I believe only solvers with a very broad skill set would have a uniform performance on the entire set. But just as different test-solvers reported being tripped up by different puzzles, competitors reported the same thing with #2 and #4 seeming to be outliers. I wonder what your experiences were?

I’m posting the first two classic puzzles below, with design spoilers concealed after each puzzle. The next two classics will follow tomorrow.

PDF

or solve online (using our beta test of Penpa-Edit tools)

PDF

or solve online (using our beta test of Penpa-Edit tools)

Themes: Both geometric and logical

Rules: Standard Sudoku rules.

Answer String: For the USSQT, the answer strings were a set of rows/columns encountered late in the puzzle. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Design Notes (highlight to view): The first puzzle was designed around a low/middle/high separation and has large squares made out of 1-3 and 7-9 only that provide some symmetry along the solve. For example, consider the 1 in the upper-right corner and the 9 in the lower-left corner which come from looking horizontally, followed by either 79 or 12 pairs to finish those border columns from looking vertically each allowing the last two numbers in the corner regions to be identified. This is probably the easiest of the four classic puzzles but not by much. The second puzzle was designed to require good use of pointing pairs, particularly in the upper-left boxes, involving the “8” and “9” that are lone digits. A relay of these pointing pairs through two boxes should place the first 8s and 9s that cascade to give several other digits.

Solutions: PDF and PDF

Results are finally posted and congratulations are due to Palmer Mebane for winning this year’s US Puzzle Championship. The closer race was for the remaining two US team spots and Jonathan Rivet was a convincing second and Will Blatt squeaked in at third. But a lot of others were one solved puzzle (or a few differences + bonus) away from a tie or being ahead. Sadly, this will be the first time in 20 years that Wei-Hwa Huang is not on the US team at a WPC (since the very 1st one in which he did not participate). His veteran leadership has helped in almost all of our team victories and it will be difficult to fill his shoes as I am now the most experienced of the US team members.

Statistics are not yet posted, but I expect to see low success percentages (20-40%) for the Number Tower and the Pathfinder puzzle. I don’t think all of these come from people spending a free guess, but often solvers will put a little time into a puzzle and then hazard the rest as the Number Tower certainly allows after you place the 3 and maybe a couple others before running into harder assignments.

The two largest surprises on the test were both Cihan Altay puzzles (which was not a surprise as his style is always “unique”). Duello was a rather interesting challenge, and was set-up to very easily break if solvers went in assuming that a 1-N number set was used for the avoided numbers. Many solvers complained about these unclear rules, but I’m left thinking that this is hardly the first time a puzzle has contained a surprise of this sort and worked well. If it weren’t for the competition pressure, I’d expect a much higher number of positive comments here. Thinking back, the 2010 USPC’s Sukazu, for example, described how numbers would be used and while many of us thought 1-4 were the likely set the puzzle managed to get other digits in there. It ended up my favorite puzzle on that test as a result. At the 2011 WPC I was less fortunate on a number square puzzle where all row/column values became a multiple of 11. It turns out 0 is a multiple of 11 in the constructor’s mind. Being stymied during the competition made me frustrated but after some rest and reevaluation it was a good fake-out too. So that this Duello puzzle quickly put a 1 at the edge of a column that with a 4 could not pack without two 0 clues was simply a typical USPC or WPC style surprise, allowed within the rules, meant to be encountered during the solve and resolved by . The puzzle is much better as a one-off style with this surprise, I think, and was certainly the author’s preference.

The Number Tower was the other surprise and the only puzzle I screwed up on the test-solve and submitted wrong, flipping the 6 and 7 (but might have caught in the extra time given competition conditions). I also posit that I might have guessed a rotation gimmick before the test if I’d had the 16 hours to think about the instructions. But I got rotation within the first minute of looking at the column certainly. It was definitely another patented “Cihan puzzle”, as he has his own creative style and exploits fonts and shapes and numbers in very creative ways while making his solvers similarly contort their brains.

The rest of the test was at a typically high quality level. Nikoli’s contributions included an interesting Sudoku (maybe a notch below their contribution from a few years back but very narrow in solving scope). Serkan had several nice solving puzzles including his Tapa and the Ambiguity with the USPC theme all over the middle that I only noticed after the test. Other US authors also had fun contributions in the Siamese Fences (Dave Tuller), Bombardoku (Adam Wood), and Pentopia (Grant Fikes), the latter being a puzzle I got to see early for this website and referred to the USPC for its good quality. As I intend to keep constructing and editing puzzles over the next year, you should probably expect me to be a constructor for the USPC again in 2014 and I hope the test is better for it. Thanks to Nick Baxter for all his work organizing the contest and to the other authors for helping put together a memorable championship.

As promised, here was the original Thermo-Skyscrapers created for the USPC. I like the visual pattern and tightness of solving path much more, but it was simply too hard to use, particularly before the practice you now have from the one you saw on the USPC from yesterday’s post.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: No given numbers, and full clue cell symmetry

Rules: Standard Skyscrapers rules. Also, as in Thermo-Sudoku, digits must be strictly increasing in all thermometer shapes from round bulb to flat end.

Answer String: Enter the seven digits inside the grid for the 7th row from left to right, followed by a comma, and then the seven digits inside the grid for the 4th column from top to bottom.

Solution: PDF

The hardest puzzle I wrote for the USPC was originally intended to be presented as a subtle “surprise”. The rules would have covered what thermometer shapes do (strictly increase from bulb to flat end), but would not have been explicit that those shapes could reach outside the grid. So finding a grid with no external numbers but with many external shapes would have been a manageable but perhaps unexpected surprise. But it was decided to just be explicit here, and with some other authors in the last few months having used the same external clue ideas with skyscrapers (including myself here with an Even/Odd Skyscrapers after I knew the fate of this puzzle) it’s not clear if this would have been unexpected anyway.

I thought this was an interesting extension of some inequality skyscraper concepts I’ve seen elsewhere. My first attempt at this puzzle type was judged very elegant and far too hard. My second attempt kept one of these two traits and made it onto the test. Like the TomTom, this variation seemed to get pretty good reviews, but I do know some solvers who fell into the trap of thinking an outside number blocked that number from appearing inside the grid.

PDF

or solve online (using our beta test of Penpa-Edit tools)

Theme: No given numbers, and full clue cell symmetry

Rules: Standard Skyscrapers rules. Also, as in Thermo-Sudoku, digits must be strictly increasing in all thermometer shapes from round bulb to flat end.

Answer String: For the USPC, the answer string was the internal cells in the 4th row and 7th row. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF

While I still want to find a good name for this variation of TomTom (Tight Fit TomTom matches the genesis story well but is probably not the best name for longevity), it was a style idea that strongly encouraged me to write for the USPC this year as it seemed a great place to debut it.

The idea actually came from Craig Kasper during a discussion of puzzle styles and possible variations. Craig didn’t think he could do it justice, but he offered it to me and I knew instantly it was a great concept to save for the future — with the USPC as the obvious first destination if it could work. I wrote two Tom/Tom puzzles (also probably not the best name — maybe in the comments people can recommend others?). The first was an easy one (10 pointer?) that became the example. The second was a tougher puzzle that has been called undervalued for 20 points by most people commenting on it. Perhaps the break-ins were not as easy to find?

The biggest struggle with the style was how to format it well; you’ll find that both of these puzzles use slashes in cells that would not normally contain the clue digit to leave more space in the fractional cells for writing numbers. Palmer’s pre-USPC example uses shaded cells and this might be a more productive route going forward. I have plans to make a bunch of TomTom variety books/puzzle packs focused on different math concepts and will probably make one around this variation when I get some larger tasks off my plate. Removing some of the extra trickiness of these samples and having simpler fractional values and even fractional clue targets should make this a good extension of TomTom puzzles for education purposes. I can even turn single cell cages into non-trivial entries!

I hope you enjoyed this variation as much as I enjoyed making it work.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between “big” sudoku and “small” number entry modes.)

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between “big” sudoku and “small” number entry modes.)

Theme: Cage geometries, and the logic of the solve and new fraction rules primarily

Rules: Variation of standard TomTom rules. The indicated ranges are larger than N x N (1-6 and 1-8 respectively), and some cells containing slashes require two digits to be placed. These cells should be treated as fractional values (top value over bottom value) for the purposes of solving the puzzle.

Answer String: For the USPC, the answer string was the 5th row and 5th column of the larger puzzle. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution 1: PDF
Solution 2: PDF

I received a lot of “pre-criticism” about having made a Counting Puzzle for the USPC. I have been rather outstated as a solver in not liking these puzzles because of the difficulty of confirming one’s answer — particularly in the old -5 point days for a mistake that would frequently cost me for even attempting and getting close to the right answer. And I often don’t get the choice to skip it when I’m close to finishing the test.

But that doesn’t mean I’ve never been called on to write Counting Puzzles. I wrote a GAMES article/Puzzlecraft chapter on the topic. And I gave it another attempt on this USPC. Call it an experiment to see if I could make anything my audience would accept as a good puzzle.

My first concept was to make a heavy path puzzle with lots of forced segments due to arrows, but not a single solution to give it a “counting” aspect. While I figured good solvers would be able to get to a “trivial” state to count a handful of total paths, all of my initial designs ended up feeling more like a broken path puzzle than a good counting puzzle so a changed goals slightly. I wondered: can I make a few very simple counting challenges work together with some simple math to be a fair challenge. Basically, something where good observation could reduce the problem into something much more tractable. And if this is testing both observation and problem solving skills in an unfamiliar setting, all the better.

Even with the “simple” format below that even had the surprise of very basic multiplication built in, the successful answer rate was quite low compared to my own expectations. And at least one solver has complained about getting 99.991% of the correct answer and getting zero credit. In my evaluation, with three small counting puzzles and a meta puzzle of building the math equation, that answer is 75% correct in the same way some of the answers in the 52k range were. All from counting one of the component puzzles one lower than expected.

So, did you think this was an appropriate USPC challenge? Did this soften or strengthen opinions against counting puzzles? Are counting puzzles still the brussel sprouts of the USPC buffet? I’ve only heard positives from people that actually got the puzzle correct so I do have to think score results often bias counting puzzle reviews (my strongly negative reviews have certainly followed my average score of -5 on these puzzles over the years).

PDF

Theme: Symmetry, mainly

Rules: Count the number of different paths from Start (S) to Finish (F). You cannot use an intersection or a path segment more than once. Path segments with arrows can only be used in the indicated direction.

Answer String: For the USPC, the answer string was the number of paths. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF

And if you want an extra challenge, solve this bonus puzzle where an arrow has been removed. It’s one step up from the original puzzle but should be just as simple to break into constituent parts if you’ve mastered the first.

Last Saturday finished another 6 week cycle of offerings from Grandmaster Puzzles. It also finished a rather busy 6 weeks of puzzle construction and testing, including three different puzzle championship rounds. Two of these have now been hosted (the US Sudoku Qualifying Test/Grand Prix Contest, and the US Puzzle Championship) and one will be a future surprise. This gives me reason to think a pause for some reflection and discussion about some of these puzzles would be a valuable use of the “gap” time before our next spurt of new puzzles and possibly new genres begins. [It also gives me a chance to hopefully address some server issues.]

The USPC is one of the few championships that follows the World Puzzle Federation’s model of puzzle balance including observational puzzles, word manipulation puzzles, and often some “trick” puzzles alongside a mix of classic constraint satisfaction types and variants. I figured — given existing contributors — that I would be most called upon to make some innovative word and observational puzzles alongside some original (read: previously unseen) variants that would hold new surprises for all solvers. The first puzzle I wanted to highlight is one that is meant to be recognizable and friendly to even the casual solver: the USPC Word Search.

I had a few ideas in mind this year for creating an interesting word search, and settled on a variety rebus gimmick where entries may or may not contain a shortened set of characters in a single square. Having previously used digit word phrases for a Sudoku Masterpieces puzzle (Some Err1ous Spelling!) and having much of that research on hand, I took my time getting a good interlinked set of “Digi2rds” together for the USPC puzzle. The missing middle shaped like an octothorpe was another goal I had in mind to give the puzzle some character. I also laid some traps around the middle for solvers trying to intuit words too soon. While many solvers will turn their noses up at a word search, I still see great value in having such puzzle styles represented on a puzzle championship. I hope I managed to give an intriguing challenge with the puzzle below.

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab mode to shift between line drawing, letter/number entry, and shading modes)

Theme: Hidden Numbers

Rules: Standard Word Search rules. Also, a digit may be used in place of its letters when spelled out. For example, “DIGIT WORD SEARCH” might appear in the grid as “DIGI2RDSEARCH”. 25 characters are missing from the grid and must be identified to complete the puzzle.

Answer String: For the USPC, the answer string was the 25 missing characters in order. For this week, you can just hit the solved button on an honor system if you think you’ve solved it.

Solution: PDF